In the figure above, ΔPQR has angle measures as shown. Is x < y?
- PQ = QR
- PR > QR
| Source | OG 2020 |
| Type | Data Sufficiency |
| Topic | Geometry |
| Sub-Topic | Triangles |
| Difficulty | Medium |
Solution
Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given
- The figure of a triangle PQR, where angle P = x°, angle Q = y° and angle R = 58°
From this information, we need to determine
- If x < y or not.
As PQR is a triangle, the sum of the three angles must be equal to 180°
- x° + y° + 58° = 180°
- Or, x° + y° = 180° – 58° = 122°
Hence, to determine whether x < y, we need to know the value of either x or y.
With this information, let us now analyse the individual statements.
Step 3: Analyse Statement 1
As per the information given in statement 1, PQ = QR.
- Therefore, we can say angle QPR = angle QRP
- Or, x° = 58°
As we can determine the value of x, we can also determine the value of y and find out whether x < y or not.
Hence, statement 1 is sufficient to answer the question.
Step 4: Analyse Statement 2
As per the information given in statement 2, PR > QR.
- Therefore, the angle opposite to PR > the angle opposite to QR
- Or, y > x
As we can determine whether x < y or not, statement 2 is sufficient to answer the question.
Step 5: Combine Both Statements Together (If Needed)
Since we could determine the answer from either of the statements individually, this step is not required.
Hence, the correct answer is option D.
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